More Information

References

Life history traits include growth rate; age and size at sexual maturity; the temporal pattern or schedule of reproduction; the number, size, and sex ratio of offspring; the distribution of intrinsic or extrinsic mortality rates (e.g., patterns of senescence); and patterns of dormancy and dispersal. These traits contribute directly to age-specific survival and reproductive functions.¹ The FLife package has a variety of methods for modelling life history traits and functional forms for processes for use in fish stock assessment and for conducting Management Strategy Evaluation (MSE).

These relationships have many uses, for example in age-structured population models, functional relationships for these processes allow the calculation of the population growth rate and have been used to to develop priors in stock assesments and to parameterise ecological models.

Quick Start

This section provide a quick way to get running and overview of what functions are available, their potential use, and where to seek help. More details are given in later sections.

The simplest way to obtain FLife is to install it from the FLR repository via the R console:

install.packages("FLife", repos = "http://flr-project.org/R")

See help(install.packages) for more details.

After installing the FLife package, you need to load it

library(FLife)

There is an example teleost dataset used for illustration and as a test dataset, alternatively you can load your own data.

data(teleost)

The dataset contains life history parameters for a range of bony fish species and families, i.e. von Bertalanffy growth parameters ( $L_{\infty}, k, t_0$ ), length at 50% mature ( $L_{50}$ ), and the length weight relationship ( $a, b$ ).

When loading a new dataset it is always a good idea to run a sanity check e.g.

is(teleost)

[1] "FLPar"     "array"     "structure" "vector"

The teleost object can be used to create vectors or other `objects with values by age using FLife methods, e.g. to construct a growth curve for hutchen (Hucho hucho)

vonB(1:10,teleost[,"Hucho hucho"])

 [1]  29.0  40.8  51.5  61.1  69.9  77.8  84.9  91.4  97.3 102.6

Plotting

Plotting is done using ggplot2 which provides a powerful alternative paradigm for creating both simple and complex plots in R using the Grammar of Graphics² The idea of the grammar is to specify the individual building blocks of a plot and then to combine them to create the desired graphic³.

The ggplot methods expects a data.frame for its first argument, data (this has been overloaded by ggplotFL to also accept FLR objects); then a geometric object geom that specifies the actual marks put on to a plot and an aesthetic that is “something you can see” have to be provided. Examples of geometic Objects (geom) include points (geom_point, for scatter plots, dot plots, etc), lines (geom_line, for time series, trend lines, etc) and boxplot (geom_boxplot, for, well, boxplots!). Aesthetic mappings are set with the aes() function and, examples include, position (i.e., on the x and y axes), color (“outside” color), fill (“inside” color), shape (of points), linetype and size.

age=FLQuant(1:20,dimnames=list(age=1:20))
len=vonB(age,teleost)

ggplot(as.data.frame(len))+
  geom_line(aes(age,data,col=iter))+
  theme(legend.position="none")

Von Bertalanffy growth curves.

Methods

There are relationships between the life history parameters and size, growth, maturation, natural mortality and productivity, as seen in the following.

Function Forms

These methods are used to create FLQuants

Growth

gascuel, gompertz, richards, vonB

Ogives

dnormal, knife, logistic, sigmoid

Natural Mortality

gislason, lorenzen

Conversions

len2wt, wt2len, ages

Population dynamics

Ecological

leslie, r

Simulation

lhPar, lhEql

Reference points

lopt, loptAge

Density Dependence

matdd, mdd

Parameter estination

moment, powh

Stationarity

rod

Random variables

rnoise

Life History Parameters

Relationship between life history traits

At a given length a large species will grow faster than a small species, for example consider the von Bertalanffy growth equation

L_{t} = L_{\infty} (1 - e^{(- k t - t_{0})})

$L_t = L_\infty (1 - e^{(-kt-t_0)})$

where $L_\infty$ is the asymptotic maximum length, $k$ is the growth coefficient, $L_t$ is length at time t, and $t_0$ the time at which an individual would, if it possible, be zero length. There is also an empirical relationship between $t_0$ and $L_{\infty}$ and $k$ i.e.

l o g (- t_{0}) = - 0.3922 - 0.2752 l o g (L_{\infty}) - 1.038 l o g (k)

$log(-t_0) = -0.3922 - 0.2752 log(L_{\infty}) - 1.038 log(k)$

Therefore for a value of $L_{\infty}$ or even $L_{max}$ the maximum size observered as $L_{\infty} ~ 0.95L_{max}$ , all the growth parameters can be recovered.

For larger species securing sufficient food to maintain a fast growth rate may entail exposure to a higher natural mortality (M). In addition, many small demersal species seem to be partly protected against predation by hiding, cryptic behaviour, being flat or by possessing spines. In their analyses of empirical estimates of natural mortality of fish, Griffiths and Harrod (2007) found species that were cryptic, hid in burrows, or had morphological defences against predators to have the lowest rates of natural mortality. Hence, at a given length individuals belonging to species with a high $L_{\infty}$ may generally be exposed to a higher M than individuals belonging to species with a low $L_{\infty}$ .

l o g (M) = 0.55 - 1.61 l o g (L) + 1.44 l o g (L_{\infty}) + l o g (k)

$log(M) = 0.55-1.61log(L) + 1.44log(L_{\infty}) + log(k)$ ## Functional forms

There are methods for creating growth curves, maturity ogives, natural mortality vectors and selection patterns.

Generation of missing life history relationships

par=lhPar(FLPar(linf=100))
par

An object of class "FLPar"
params
      linf          k         t0          a          b      ato95 
 100.00000    0.16531   -0.10000    0.00030    3.00000    1.00000 
       a50       asym         bg         m1         m2         a1 
   4.35996    1.00000    3.00000  217.35644   -1.61000    4.35996 
        sl         sr          s          v 
   2.00000 5000.00000    0.90000 1000.00000 
units:  NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

Simulation

Simulation of equilibrium values and reference points

library(FLBRP)
eql=lhEql(par)

ggplot(FLQuants(eql,"m","catch.sel","mat","catch.wt"))+
  geom_line(aes(age,data))+
  facet_wrap(~qname,scale="free")+
  scale_x_continuous(limits=c(0,15))

Age-vectors of growthm natural mortality, maturity and selection pattern

Equilibrium curves and reference points.

An object of class "FLPar"
params
        r        rc       msy      lopt        sk      spr0    sprmsy 
 0.394344  0.139678 53.644110 63.520418  0.195428  0.120826  0.026313 
units:  NA NA NA NA NA NA NA

Creation of FLBRP objects

Stock recruitment relationships

Stock recruitment relationships for a steepness of 0.75 and vigin biomass of 1000

Production curves, Yield v SSB, for a steepness of 0.75 and vigin biomass of 1000.

Density Dependence

Modelling density dependence in natural mortality and fecundity.

library(FLBRP)

par=teleost[,"Hucho hucho"]
par=lhPar(par)
hutchen=lhEql(par)
 
scale=stock.n(hutchen)[,25]%*%stock.wt(hutchen)
scale=(stock.n(hutchen)%*%stock.wt(hutchen)%-%scale)%/%scale
 
m=mdd(stock.wt(hutchen),par=FLPar(m1=.2,m2=-0.288),scale,k=.5)   

ggplot(as.data.frame(m))+
   geom_line(aes(age,data,col=factor(year)))+
   theme(legend.position="none")+
    scale_x_continuous(limits=c(0,15))

Density Dependence in M

scale=stock.n(hutchen)[,25]%*%stock.wt(hutchen)
scale=(stock.n(hutchen)%*%stock.wt(hutchen)%-%scale)%/%scale

mat=matdd(ages(scale),par,scale,k=.5)   
 
ggplot(as.data.frame(mat))+
    geom_line(aes(age,data,col=factor(year)))+
    theme(legend.position="none")+
    scale_x_continuous(limits=c(0,15))

Density Dependence in M

Noise

Methods to simulate random noise with autocorrelation, e.g. by age or cohort

MSE using empirical HCR

Estimation

Life history parameters can also be used to estimate quantities of use in stock assessment

Beverton and Holt (1956) developed a method to estimate life history and population parameters length data. e.g.

Z = K \frac{L_{\infty} - \bar{L}}{\bar{L} - L^{'}}

$\begin{equation}Z=K\frac{L_{\infty}-\overline{L}}{\overline{L}-L^\prime} \end{equation}$

Based on which Powell (1979) developed a method, extended by Wetherall, Polovina, and Ralston (1987), to estimate growth and mortality parameters. This assumes that the right hand tail of a length frequency distribution was determined by the asymptotic length $L_{\infty}$ and the ratio between Z and the growth rate k.

The Beverton and Holt methods assumes good estimates for K and $L_{\infty}$ , while the Powell-Wetherall method only requires an estimate of K, since $L_{\infty}$ is estimated by the method as well as Z/K.These method therefore provide estimates for each distribution of Z/K, if K is unknown and Z if K is known.
%As well as assuming that growth follows the von Bertalanffy growth function, it is also assumed that the population is in a steady state with constant exponential mortality, no changes in selection pattern of the fishery and constant recruitment. In the Powell-Wetherall method $L^\prime$ can take any value between the smallest and largest sizes. Equation 1 then provides a series of estimates of Z and since

\bar{L} - L^{'} = a + b L^{'}

$\begin{equation}\overline{L}-L^\prime=a+bL^{\prime} \end{equation}$ a and b can be estimated by a regression analysis where

b = \frac{- K}{Z + K}

$\begin{equation}b=\frac{-K}{Z+K} \end{equation}$

a = - b L_{\infty}

$\begin{equation}a=-bL_{\infty} \end{equation}$

Therefore plotting $\overline{L}-L^\prime$ against $L^\prime$ therefore provides an estimate of $L_{\infty}$ and Z/K

Plotting $\overline{L}-L^\prime$ against $L^\prime$ provides an estimate of $L_{\infty}$ and Z/k, since $L_{\infty}=-a/b$ and $Z/k=\frac{-1-b}{b}$ . If k is known then it also provides an estimate of Z ( ).

  age   obs    hat    sel
1   1 32356 249252 0.0136
2   2 49911 152624 0.0342
3   3 69038  93457 0.0773
4   4 45627  57226 0.0834
5   5 32732  35041 0.0977
6   6  8910  21457 0.0434

Catch curve analysis

data(ple4)
ctc=as.data.frame(catch.n(ple4))
ctc=ddply(ctc,.(year), with, cc(age=age,n=data))
ctc=ddply(transform(ctc,decade=factor(10*(year%/%10))),.(decade,age),with,data.frame(sel=mean(sel)))
ggplot(ctc)+
  geom_line(aes(age,sel,colour=decade))

More Information

You can submit bug reports, questions or suggestions on FLife at the FLife issue page,⁴ or on the FLR mailing list.
Or send a pull request to https://github.com/lauriekell/FLife/
For more information on the FLR Project for Quantitative Fisheries Science in R, visit the FLR webpage.⁵
The latest version of FLife can always be installed using the devtools package, by calling

    library(devtools)
    install_github("lauriekell/FLife")

Software Versions

R version 3.3.2 (2016-10-31)
FLCore: 2.6.0.20160707
FLife: 2.1.1
Compiled: Fri Feb 17 09:33:34 2017
Git Hash: 563ca51

Author information

Laurence KELL. laurie@kell.es

References

Beverton, R.J.H., and S.J. Holt. 1956. “Review of Method for Estimating Mortality Rates in Exploited Fish Populations, with Special Reference to Sources of Bias in Catch Sampling.” Rapports et Proces-Verbaux. 140 (1): 67–83.

Powell, David G. 1979. “Estimation of Mortality and Growth Parameters from the Length Frequency of a Catch [Model].” Rapports et Proces-Verbaux Des Reunions 175.

Wetherall, JA, JJ Polovina, and S. Ralston. 1987. “Estimating Growth and Mortality in Steady-State Fish Stocks from Length-Frequency Data.” ICLARM Conf. Proc, 53–74.

http://www.oxfordbibliographies.com/view/document/obo-9780199830060/obo-9780199830060-0016.xml ↩
Wilkinson, L. 1999. The Grammar of Graphics, Springer. doi 10.1007/978-3-642-21551-3_13.↩
http://tutorials.iq.harvard.edu/R/Rgraphics/Rgraphics.html ↩
https://github.com/lauriekell/FLife/issues ↩
http://flr-project.org ↩

Life History Relationships

17 febrero, 2017

Quick Start

Plotting

Methods

Function Forms

Growth

Ogives

Natural Mortality

Conversions

Population dynamics

Ecological

Simulation

Reference points

Density Dependence

Parameter estination

Stationarity

Random variables

Life History Parameters

Simulation

Simulation of equilibrium values and reference points

Stock recruitment relationships

Density Dependence

Noise

MSE using empirical HCR

Estimation

Catch curve analysis

More Information

Software Versions

Author information

References